- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] f(true,x,y,z) -> f(gt(x,plus(y,z)),x,s(y),z)
[2] f(true,x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z))
[3] plus(n,0) -> n
[4] plus(n,s(m)) -> s(plus(n,m))
[5] gt(0,v) -> false
[6] gt(s(u),0) -> true
[7] gt(s(u),s(v)) -> gt(u,v)


Sub problem: 
guided: 

DP termination of:
<Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,s(y),z)>
<Marked_f(true,x,y,z) , Marked_gt(x,plus(y,z))>
<Marked_f(true,x,y,z) , Marked_plus(y,z)>
<Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,y,s(z))>
<Marked_f(true,x,y,z) , Marked_gt(x,plus(y,z))>
<Marked_f(true,x,y,z) , Marked_plus(y,z)>
<Marked_plus(n,s(m)) , Marked_plus(n,m)>
<Marked_gt(s(u),s(v)) , Marked_gt(u,v)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,y,s(z))> 
      --> <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,y,s(z))>
  <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,y,s(z))> 
     --> <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,s(y),z)>
  <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,s(y),z)> 
     --> <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,y,s(z))>
  <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,s(y),z)> 
     --> <Marked_f(true,x,y,z) , Marked_f(gt(x,plus(y,z)),x,s(y),z)>
}

{  <Marked_plus(n,s(m)) , Marked_plus(n,m)> 
      --> <Marked_plus(n,s(m)) , Marked_plus(n,m)>
}

{  <Marked_gt(s(u),s(v)) , Marked_gt(u,v)> 
      --> <Marked_gt(s(u),s(v)) , Marked_gt(u,v)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  f(true,x,y,z) >= f(gt(x,plus(y,z)),x,s(y),z) ;
  f(true,x,y,z) >= f(gt(x,plus(y,z)),x,y,s(z)) ;
  gt(s(u),s(v)) >= gt(u,v) ;
  gt(s(u),0) >= true ;
  gt(0,v) >= false ;
  plus(n,s(m)) >= s(plus(n,m)) ;
  plus(n,0) >= n ;
  Marked_f(true,x,y,z) >= Marked_f(gt(x,plus(y,z)),x,s(y),z) ;
  Marked_f(true,x,y,z) >= Marked_f(gt(x,plus(y,z)),x,y,s(z)) ;
 }
 + Disjunctions:{ 
{
  Marked_f(true,x,y,z) > Marked_f(gt(x,plus(y,z)),x,s(y),z) ;
 }
{
  Marked_f(true,x,y,z) > Marked_f(gt(x,plus(y,z)),x,y,s(z)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  f(true,x,y,z) >= f(gt(x,plus(y,z)),x,s(y),z) ;
  f(true,x,y,z) >= f(gt(x,plus(y,z)),x,y,s(z)) ;
  gt(s(u),s(v)) >= gt(u,v) ;
  gt(s(u),0) >= true ;
  gt(0,v) >= false ;
  plus(n,s(m)) >= s(plus(n,m)) ;
  plus(n,0) >= n ;
  Marked_f(true,x,y,z) > Marked_f(gt(x,plus(y,z)),x,s(y),z) ;
  Marked_f(true,x,y,z) > Marked_f(gt(x,plus(y,z)),x,y,s(z)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  f(true,x,y,z) >= f(gt(x,plus(y,z)),x,s(y),z) ;
  f(true,x,y,z) >= f(gt(x,plus(y,z)),x,y,s(z)) ;
  gt(s(u),s(v)) >= gt(u,v) ;
  gt(s(u),0) >= true ;
  gt(0,v) >= false ;
  plus(n,s(m)) >= s(plus(n,m)) ;
  plus(n,0) >= n ;
  Marked_f(true,x,y,z) > Marked_f(gt(x,plus(y,z)),x,s(y),z) ;
  Marked_f(true,x,y,z) > Marked_f(gt(x,plus(y,z)),x,y,s(z)) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
No solution found for these parameters.(573 bt (41) [456])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 3.426788 seconds (real time)
Cime Exit Status: 0